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Full-Text Articles in Physical Sciences and Mathematics
Nonparametric Derivative Estimation Using Penalized Splines: Theory And Application, Bright Antwi Boasiako
Nonparametric Derivative Estimation Using Penalized Splines: Theory And Application, Bright Antwi Boasiako
Doctoral Dissertations
This dissertation is in the field of Nonparametric Derivative Estimation using
Penalized Splines. It is conducted in two parts. In the first part, we study the L2
convergence rates of estimating derivatives of mean regression functions using penalized splines. In 1982, Stone provided the optimal rates of convergence for estimating derivatives of mean regression functions using nonparametric methods. Using these rates, Zhou et. al. in their 2000 paper showed that the MSE of derivative estimators based on regression splines approach zero at the optimal rate of convergence. Also, in 2019, Xiao showed that, under some general conditions, penalized spline estimators …
Inverse Probability Weighting In Survival Analysis And Network Analysis, Yukun Lu
Inverse Probability Weighting In Survival Analysis And Network Analysis, Yukun Lu
Doctoral Dissertations
Inverse probability weighting is a popular technique to accommodate selection bias due to non-random sampling and missing data. In the first chapter, we develop an inverse probability weighted estimator and an augmented inverse probability weighted estimator of regression coefficients for a linear model with randomly censored covariates, when the censoring mechanism may be dependent on the outcome. We investigate the asymptotic properties of both estimators and evaluate their finite sample performance through extensive simulation studies. We apply the proposed methods to an Alzheimer’s disease study. In the second chapter, we present an application of network analysis in a study of …